Seminar on Numerical Analysis

letzte Änderung: 2021-09-30
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Seminar on Numerical Analysis

Elliptic Problems on Non-smooth Domains and their Numerical Approximation

(Course Id 327.014, 2 hours per week, semester 5)

Supervisors: A.Univ.-Prof. Dr. Helmut Gfrerer

                       O.Univ.-Prof. Dr. Ulrich Langer

                       A.Univ.-Prof. Dr. Walter Zulehner

Start of the seminar: Tue, 2013-10-08, 13:45 - 15:15 Uhr, Room: S2 059

Time, room, seminar, student, supervisor:

Tue, 2013-10-0813:45 - 15:15 Room: S2 059IntroductionW. Zulehner
Tue, 2013-10-2215:30 - 17:00 Room: S2 059Seminar 01J. HöllerW. Zulehner
Tue, 2013-10-2915:30 - 17:00 Room: S2 059Seminar 02N. BayramovW. Zulehner
Tue, 2013-11-0515:30 - 17:00 Room: S2 059Seminar 03K. RafetsederW. Zulehner
Tue, 2013-11-1215:30 - 17:00 Room: S2 059Seminar 04W. KrendlH. Gfrerer
Tue, 2013-11-2615:30 - 17:00 Room: S2 059Seminar 05P. GanglH. Gfrerer
Tue, 2013-12-0315:30 - 17:00 Room: S2 059Seminar 06S. MooreU. Langer
Tue, 2013-12-1015:30 - 17:00 Room: S2 059Seminar 07A. FohlerU. Langer
Tue, 2014-01-0715:30 - 17:00 Room: S2 059Seminar 08N. BayramovU. Langer
Tue, 2014-01-1415:30 - 17:00 Room: S2 059Seminar 09A. Fohler, S. MooreU. Langer
Tue, 2014-01-2115:30 - 17:00 Room: S2 059Seminar 10J. Höller, K. RafetsederW. Zulehner
Tue, 2014-01-2815:30 - 17:00 Room: S2 059Seminar 11P. Gangl, W. KrendlW. Zulehner


- Seminar Topics up

Introduction:2013-10-08
Introduction by Walter Zulehner
Seminar 01:2013-10-22
Title: Boundaries and traces
Literature:   [2] pp. 11 - 23
Supervisor: W. Zulehner
Student:     J. Höller
Seminar 02:2013-10-29
Title: Green's formula and density results
Literature:    [2] pp. 24 - 34
Supervisor: W. Zulehner
Student:     N. Bayramov
Seminar 03:2013-11-05
Title: Variational solutions and classical regularity results
Literature:    [2] pp. 36 - 43
Supervisor: W. Zulehner
Student:     K. Rafetseder
Seminar 04:2013-11-12
Title: Fredholm property in 2D
Literature:    [2] pp. 43 - 49
Supervisor: H. Gfrerer
Student:     W. Krendl
Seminar 05:2013-11-26
Title: Vertex behavior in 2D
Literature:    [2] pp. 49 - 59
Supervisor: H. Gfrerer
Student:     P. Gangl
Seminar 06:2013-12-03
Title: Edge behavior in 3D
Literature:    [2], pp. 60 - 72
Supervisor: U. Langer
Student:     S. Moore
Seminar 07:2013-12-10
Title: Vertex behavior in 3D
Literature:    [2], pp. 72 - 81
Supervisor: U. Langer
Student:     A. Fohler
Seminar 08:2013-01-07
Title: Singular basic functions
Literature:    [3], pp. 252 - 272
Supervisor: U. Langer
Student:     N. Bayramov
Seminar 09:2014-01-14
Title: Mesh grading I - Moore
   Mesh grading II - Fohler
Literature:    [3], pp. 273 - 287
Supervisor: U. Langer
Students:     A. Fohler, S. Moore
Seminar 10:2014-01-21
Title: Zenger Correction I - Höller
   Zenger Correction II - Rafetseder
Literature:    [4], [5]
Supervisor: W. Zulehner
Students:     J. Höller, K. Rafetseder
Seminar 11:2014-01-28
Title: Brenner's Approach I - Gangl
   Brenner's Approach II - Krendl
Literature:    [6]
Supervisor: W. Zulehner
Students:     P. Gangl, W. Krendl


- Literature up

[1]   P. Grisvard. Elliptic Problems in Nonsmooth Domains. SIAM (2011)
[2]   P. Grisvard. Singularities in Boundary Value Problems. Masson (1992)
[3]   L.A. Oganesjan, L.A. Puchovetz. Variational difference methods for the solution of elliptic equations. Isdatelstvo Akademi Nank Armjanskoj SSP, Erevan 1979 (in Russian)
[4]   C. Zenger, H. Gietl. Improved Difference Schemes for the Dirichlet Problem of Poisson's Equation in the Neighbourhood of Corners.
[5]   U. Rüde. Zur numerischen Behandlung von Singularitäten in elliptischen partiellen Differentialgleichungen. Dissertation, TU München, 1988.
[6]   S. Brenner. Multgrid Methods for the Computation of Singular Solutions and Stress Intensity Factors I: Corner Singularities.

- Participants up

Bayramov Nadir
Fohler Armin
Gangl Peter
Höller Johannes
Krendl Wolfgang
Moore Stephen
Rafetseder Katharina

- General Remarks up